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6-8 Accelerated 7 Unit 8 Lesson 12

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Lesson 12

12.1 Warm-up 12.2 Activity 12.3 Activity 12.4 Activity Student Lesson Summary Glossary

Unit 8, Lesson 12

Edge Lengths, Volumes, and Cube Roots

Accelerated 7

12.1

Warm-up

Ordering Squares and Cubes

Let , , , , , and be positive numbers.

Given these equations, arrange , , , , , and from least to greatest. Explain your reasoning.

Are You Ready for More?

12.2

Activity

Card Sort: Rooted in the Number Line

Your teacher will give you a set of cards. Each card has a number line with a plotted point, an equation, or a square or cube root value.

For each card with a letter and square or cube root value, match it with the location on a number line where the value exists, and the equation that the value makes true. Record your matches and be prepared to explain your reasoning.

Are You Ready for More?

12.3

Activity

Cube Root Values

The value of a cube root of a number lies between two integers. Which are those consecutive whole numbers for the following? Be prepared to explain your reasoning.

Are You Ready for More?

12.4

Activity

Solutions on a Number Line

The numbers , , and are positive, and:

A number line that shows the integers from negative 3 to 9

Plot , , and on the number line. Be prepared to share your reasoning with the class.
Plot on the number line.

Are You Ready for More?

Student Lesson Summary

For a square, its side length is the square root of its area. For example, this square has an area of 16 square units and a side length of 4 units.

Both of these equations are true:

A square with a side length of 4 units on a square grid.

For a cube, the edge length is the cube root of its volume. For example, this cube has a volume of 64 cubic units and an edge length of 4 units:

Both of these equations are true:

A solid cube composed of 64 unit cubes. Each edge length is 4 unit cubes.

is pronounced “the cube root of 64.”

Like square roots, most cube roots of whole numbers are irrational. The only time the cube root of a number is a rational number is when the number we are taking the cube root of is a perfect cube. For example, 8 is a perfect cube, and .

We can approximate the values of the cube root of a number by observing the integers around it and remembering the relationship between cubes and cube roots. For example, is between 2 and 3 since and , and 20 is between 8 and 27. Similarly, since 100 is between and , we know is between 4 and 5.

Glossary

cube root

The cube root of a number is the number whose cube is . It is also the edge length of a cube with a volume of . The cube root of is written as .

The cube root of 64 is written as . Its value is 4 because is 64.

is also the edge length of a cube that has a volume of 64.